Date of Award


Document Type


Degree Name

Master of Science


Department of Electrical and Computer Engineering

First Advisor

Stephen C. Cain, PhD.


A phase retrieval algorithm designed for use with under-sampled astronomical data is developed in this thesis. Blind-deconvolution, Gerchberg Saxton (GS), and a field-based compass search are combined into an algorithm capable of recovering Zernike coefficients 4 through 11 from single frames of noisy, under-sampled data without the need to unwrap the recovered phase. The performance of the algorithm in data under-sampled by a factor of 2 is compared the performance of the algorithm on Nyquist-sampled data. In simulation trials, the magnitudes of all 8 estimated Zernike coefficients converged to within half a wave of the true values for 98% of the Nyquist-sampled frames and 92% under-sampled frames. The simulation was conducted using 100 frames of point-source data generated by randomly choosing Zernike coefficients 2 through 11 from a normal distribution. Phase retrieval was performed on defocused data and data containing an astigmatism aberration. For the astigmatism data, the estimated Zernike coefficient magnitudes were within 1/10th of a wave for Nyquist data and 1/5th of a wave for data under-sampled by a factor of 2. The magnitude of defocus recovered from Nyquist-sampled data was within 0.02 waves of the value predicted using defocus recovered from data under-sampled by 2.

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